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Worksheet: Exponential Growth

In this worksheet, we will practice applying exponential growth in real-life situations.

Q1:

A mathematical model predicts that the population of a city, 𝑥 million,
will be given by the formula 𝑥=2(1.22)𝑛,
where 𝑛 is the number of years from now.
What does the model predict the population will be in 2 years’ time?

Q2:

At the end of 2000,
the population of a country was 22.4 million.
Since then, the population has increased by 5.6% every year. What
is the population, rounded to the nearest tenth, of the country at the end of 2037?

Q3:

David has 73 rabbits. He believes that he will have
rabbits after months. How many rabbits does he
expect to have 2 months from now?

A635 rabbits

B200 rabbits

C634 rabbits

D191 rabbits

Q4:

The population of a city increases by 4% every year. How
many years does it take for the population of the city to double?

Q5:

A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees.
To the nearest year, how long ago was the wood for the artifact cut from the tree? Note that the half-life of carbon-14 is
5730 years.

Q6:

A bacterial colony’s population doubles every
5 hours. How long does it take to triple? Give the result to
the nearest one decimal place.

Q7:

A cattle farm has 25 cows.
The farmer predicts that each year he will have 19% more cows than the year before.
How many cows, to the nearest whole number, will he have after
7 years?

Q8:

An area covered in green algae was found on July 5 on the bottom of a swimming pool.
The area, in square millimeters, the algae covers 𝑡 days later is given by
𝐴=1.2⋅2𝑡3.

What does 1.2 represent?

AIt is the time to reach the bottom of the swimming pool.

BIt is the time taken by the algae to cover that area on July 5.

CIt is the area in square millimeters of the swimming pool.

DIt is the area in square millimeters covered by the algae on July 5.

EIt is the number of days needed for the algae to cover the bottom of the swimming pool.

What does 2𝑡3 mean?

AThe area covered by the algae doubles every three days.

BThe area covered by the algae triples every day.

CThe area covered by the algae doubles every day.

DThe area covered by the algae triples every two days.

EThe area covered by the algae doubles every third of a day.

Q9:

A microorganism reproduces by binary fission, where every hour each cell divides into two cells. Given that there are 24 431 cells to begin with, determine how long it will take for
there to be 97 724 cells.

Q10:

The population of a city is growing according to the equation 𝑥=9(1.79)𝑛,
where 𝑥 is the population in millions, and 𝑛 is the number of years since 2015. What was the population of the city in 2015?

Q11:

The population of Malawi,
in millions, between
1960 and
2016
can be modeled by the function
𝑃(𝑡)=3.621.029𝑡.
By how much has the average rate of growth changed
from the period
1960 to
1965 to the period
2011
to 2016?
Give your answer in thousands per year to the nearest thousand.

A112000

B500000

C245000

D367000

E388000

Q12:

In 1970,
the world population was 3.682 billion and showed a growth rate of 2.08% per year.
Assuming a constant growth rate,
what would have been the estimate for the size of the population in 2017?
Give your answer accurate to four significant figures.